A number pyramid looks like a wall of bricks with a few bricks missing. It has one rule, and once you see it, you can solve most of these puzzles with two small moves. Let's climb one together.
The one rule
Every brick holds the sum of the two bricks directly below it. That is all. Here is the rule on its smallest wall.
3 + 5 = 8
The two bricks on the bottom add up to the brick above them. Walls can be as tall as nine rows, but every brick follows this same rule.
Our puzzle, one move at a time
Here is a five-row wall. Seven bricks are filled in. The question marks are what we need to find. Look for any row where the bricks below are already known.
The puzzle
The top brick is 83. The bottom row shows 2, 7, 2 and 9, and the last bottom brick is missing. One brick in the fourth row is given as 14.
Add up where you can
In the fourth row, three bricks sit on two known bricks. 2 + 7 = 9, then 7 + 2 = 9, then 2 + 9 = 11. These are the easy ones. Fill them in.
Subtract down when a brick is missing
The brick marked 14 sits on 9 and a missing brick. So 9 + ? = 14, which means ? = 14 − 9 = 5. Adding goes up the wall. Subtracting goes down.
Keep climbing
Now the third row is easy: 9 + 9 = 18, 9 + 11 = 20 and 11 + 14 = 25. Each finished row hands you the row above it.
Finish at the top
One brick is left in the second row: 20 + 25 = 45. Check the summit: 38 + 45 = 83, exactly the number we were given. The wall holds together.
Check your work like an explorer
Every brick you fill can be checked against the one above it, so you never have to wonder whether you are right. If a row does not add up to the brick above, one number below it is wrong. Fix that one first.
Three habits that make it faster
- Scan for rows with two known neighbours. Those bricks fill themselves in.
- Use a known brick above and one below. The missing brick is the difference between them.
- Write small, in pencil. A wall often needs a second look at a number you wrote early.
A taste of the real thing
In Escape the Pyramid, every chamber is a puzzle page, and the answer in the door brick tells you which page to turn to next. Plain number pyramids are one kind of chamber. The same pages also hide other kinds, shown here from Level 1.
Books mentioned
Escape the Pyramid, Level 1
A math escape book with 45 locked chambers. Number pyramids like the one above are one of its 5 puzzle kinds, so the book is not all pyramids. The other four are number trails, wrong-brick hunts, picture bricks and ink blots.
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Escape the Pyramid, Level 2
The same adventure with harder chambers. Number pyramids are one of its 8 puzzle kinds, joined by mixed-sign pyramids, four-operation pyramids and match-moving puzzles.
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